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Mirrors > Home > MPE Home > Th. List > vtocle | Structured version Visualization version GIF version |
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993.) |
Ref | Expression |
---|---|
vtocle.1 | ⊢ 𝐴 ∈ V |
vtocle.2 | ⊢ (𝑥 = 𝐴 → 𝜑) |
Ref | Expression |
---|---|
vtocle | ⊢ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtocle.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | vtocle.2 | . . 3 ⊢ (𝑥 = 𝐴 → 𝜑) | |
3 | 2 | vtocleg 3428 | . 2 ⊢ (𝐴 ∈ V → 𝜑) |
4 | 1, 3 | ax-mp 5 | 1 ⊢ 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1630 ∈ wcel 2144 Vcvv 3349 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1869 ax-4 1884 ax-5 1990 ax-6 2056 ax-7 2092 ax-9 2153 ax-12 2202 ax-ext 2750 |
This theorem depends on definitions: df-bi 197 df-an 383 df-tru 1633 df-ex 1852 df-sb 2049 df-clab 2757 df-cleq 2763 df-clel 2766 df-v 3351 |
This theorem is referenced by: zfrepclf 4908 tz6.12i 6355 eloprabga 6893 cfflb 9282 axcc3 9461 nn0ind-raph 11678 finxpreclem6 33563 |
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